36 ideas
23755 | Genius and love of truth are always accompanied by great humility [Weil] |
15102 | S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
15103 | Blackburn fails to show that the necessary cannot be grounded in the contingent [Cameron] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
23747 | What is sacred is not a person, but the whole physical human being [Weil] |
23756 | The mind is imprisoned and limited by language, restricting our awareness of wider thoughts [Weil] |
23758 | Beauty is an attractive mystery, leaving nothing to be desired [Weil] |
23760 | All we need are the unity of justice, truth and beauty [Weil] |
23748 | The sacred in every human is their expectation of good rather than evil [Weil] |
23759 | Everything which originates in love is beautiful [Weil] |
23762 | Evil is transmitted by comforts and pleasures, but mostly by doing harm to people [Weil] |
23750 | It is not more money which the wretched members of society need [Weil] |
23749 | The problem of the collective is not suppression of persons, but persons erasing themselves [Weil] |
23753 | People absurdly claim an equal share of things which are essentially privileged [Weil] |
23752 | Giving centrality to rights stifles all impulses of charity [Weil] |
23751 | Rights are asserted contentiously, and need the backing of force [Weil] |
23757 | The spirit of justice needs the full attention of truth, and that attention is love [Weil] |
23761 | Justice (concerning harm) is distinct from rights (concerning inequality) [Weil] |
23764 | The only thing in society worse than crime is repressive justice [Weil] |
23763 | Punishment aims at the good for men who don't desire it [Weil] |
15104 | The 'moving spotlight' theory makes one time privileged, while all times are on a par ontologically [Cameron] |
23754 | The only choice is between supernatural good, or evil [Weil] |